Exporting Parts of mesh
Afaik no, but it could also depend on the specific exporter, since they are all independent (made differently). 

eg: the collada exporter has a specific option.



The simplest way to get what you need is to save your file, then create a new empty blend file and import in it from the saved file where you have only what you want (eg chest piece).

Then, even without saving the new file, export from that new file to th eformat you need (eg: obj, dxf, fbx, etc.).